Structure of the Matter PDF

CHAPTER I: STRUCTURE OF THE MATTER I.1. Constitution of the atom I.1.1. Introduction. The matter that surrounds us consists of atoms. Atom’ comes from the Greek ‘atomos’ meaning indivisible. We currently believe that the atom is the basic unit of matter, which consists of a den...

CHAPTER I: STRUCTURE OF THE MATTER I.1. Constitution of the atom I.1.1. Introduction. The matter that surrounds us consists of atoms. Atom’ comes from the Greek ‘atomos’ meaning indivisible. We currently believe that the atom is the basic unit of matter, which consists of a dense nucleus surrounded by a cloud of negatively charged electrons. The nucleus contains a mix of positively charged protons and electrically neutral neutrons. The atom is indivisible, unbreakable; quantity of infinitely small matter. The atom consists of elementary particles: the nucleus (the atom’s central core) and electronic cloud (electrons). Electron, proton and the neutron are called fundamental subatomic particles). The atom is a very small quantity of matter whose dimensions are of the order 10-10 m (Angstrom) and its mass is of the order of 10-26 kg We have: 1A0 = 10-10 m 1nm= 10-9m A. The nucleus: The nucleus is composed of neutrons and protons, which are nucleons. Protons (noted p) and neutrons (noted n) have substantially the same mass. The nucleus is composed of neutrons (mn=1,6749.10-27kg) and protons (mp = 1.6726.10-27kg), so it is positively charged. The electric charge of a proton is called elementary charge, it is noted e. With: e = 1.6 10-19 Coulomb. The proton and the neutron are called nucleons. The charge of the nucleus is equal to the number of protons «Z» multiplied by the charge of the proton, (Q nucleus= Z* e) B. The electronic cloud: The electronic cloud is composed of electrons, noted e. The electron has a negative charge equal 1 e = - 1.6 10-19 C. The mass of the electron is me = 9.109 10-31 kg, about 2000 times lower than that of protons and neutrons, it will often be negligible. The charge of an electronic cloud is equal to the number of electrons «Z» multiplied by the charge of the electron (-e ). Q cloud= Z * (-e).. I.2. Characteristics of the atom: The atom is characterized by: A. Number of charge or atomic number Z: The number of charge of an atom, the number Z of protons or electron. The atomic number (Z): number of protons contained in the nucleus of each atom of an element. This number Z determines the nature of an element.  In an atom (neutral entity), the number of protons is equals the number of electrons. Example: Nitrogen Z=7 each N atom has 7 protons and 7 electrons.  It is the nucleus of the atom, which determines the belonging of the given element. B. Mass number (atomic mass) A The mass number (atomic number) A, represents the number of nucleons (total number of protons and neutrons). We have A = Z+N avec A: mass number, Z (number of protons or electrons), N: number of neutrons. The difference A - Z = N gives the number of neutrons in the nucleus of the atom. Z give also the number of electrons in the atom. Example: The carbon atom is represented by: Z = 6 So this carbon atom has 6 protons in the nucleus and also 6 electrons around the nucleus. A = 12 this means The nucleus of the carbon atom contains 12 nucleons 6 protons and 6 neutrons. C. Symbolic representation of the atom A An atom is represented symbolically by ZX but this symbol more precisely designates the nucleus of the chemical element “X” because: The number of nucleons present in the nucleus is the sum of protons and neutrons. Z : is called the atomic number and represents the number of protons in the nucleus of the atom. Definition of the Nuclide: It is an atom type, which characterized by Z (protons or electrons) and N (neutrons), a couple of these two values define a nuclide. 2 Remarks:  The mass of the electron is about 2000 times weaker than that of a nucleon.  The mass of the atom concentrated at the nucleus because 𝑚𝑒 − negligible in front 𝑚𝑝 or 𝑚𝑛.  Nucleons form almost all the mass of the atom.  The mass of an atomic nucleus is always slightly less than the sum of the masses of its nucleons. The difference Δm between the mass of nucleons and that of the nucleus is called «mass defect». The amount of ΔE corresponding energy (ΔE= Δm.C2 , is called the energy that would be released if the nucleus is formed from its nucleons. D. The atomic molar mass The atomic molar mass of an element or the mass of one mole of atoms is the relative atomic mass (Ar) expressed in grams per mole.  The symbol is M  Unit is gram per mole = g.mol -1 E. Molar mass of a molecule This molar mass is equal to the sum of the molar masses of the atoms constituting the molecule. Example: Mm H2SO4= 2×MmH+ MmS + MmO = (2×1)+32+4×(16) = 98 g/mole  AVOGADRO constant (Number of AVOGADRO) The number of Avogadro is the number of elementary entities (atoms, ions or molecules) contained in a mole of these same entities. In other words, it corresponds to the number of carbon atoms contained in 12 grams of carbon 12, approximately N= 6.022 x 1023.  The unit of atomic mass It is a standard unit of measurement, used to express the mass of elementary particles (very small), it is the unit of measurement most suitable for small particles. Atomic mass units are often used to describe an element’s atomic weight. We have 1 u.m.a = 1.66.10-27Kg.  Isotopes: Isotopes are defined as nuclides that have the same Z but a different atomic mass (number of masses) “A” so different number of neutrons. Natural elements are usually mixtures of isotopes. Only a small fraction of the isotopes is known to be stable indefinitely. All the others disintegrate spontaneously with the release of energy by processes. There are about 3000 nuclides either stable or radioactive. 3  Average atomic mass of an element: It is the mass of this element in U.m.a taking into account its isotopes, it is given by the following formula 𝑴 = 𝜮 𝑿𝒊 × 𝑴𝒊⁄𝑿𝒊 With X1, X2, X3, … (Abundance of different isotopes of the element) M1, M2, M3, … (atomic mass of different isotopes) 1.3. Binding and cohesion energies of the nucleus I.3.1: Nucleus binding energy. It is the energy necessary for the formation of any nucleus from particles. We consider the following reaction Z + N → Z AX+E If E is negative, then the nucleus is stable. Mass balance Δm = m2-m1 with m1 masses of proton+ neutron m2 nucleus mass = atom mass – electron mass Formation of the nucleus, Δm < 0 ‘mass defect” Example 1 Formation enrgy of deuterium nucleus ΔE E1 Conclusion: Bohr’s theory, despite its remarkable success on hydrogen and hydrogenoid, could not explain the spectra of multi-electron atoms because Bohr did not take into account the new electron-electron, electron-nucleus repulsion forces. This theory gave way in the 1920 to the theory of quantum mechanics. 10 I.6.Quantum models developed in quantum mechanics I.6.1. Broglie 1924 Hypothesis: By analogy with light, Broglie postulated the wave-corpuscle duality, which does not apply only to light, but it can be generalized to any movement of a corpuscle of mass m and speed v: ℎ𝑐 For light, E = hδ= = ……. 1 𝜆 According to Einstein E=mc²………2 ℎ ℎ𝑐 ℎ 1=2 = 𝑚𝑐² = 𝑚𝑐 𝜆 = 𝑚𝑐 𝜆 𝜆 For an electron in motion comparable to a wave ℎ ℎ 𝜆 = 𝑚𝑣 , mv= amount of movement, p=mv so 𝜆 = 𝑝 I.5.2. Heisenberg uncertainty principle: It is not possible to know with absolute precision the position and the speed of an electron at a given moment, their determination always supposes an uncertainty Δx × Δp > ћ ℎ ћ = 2𝜋 ћ: mean Planck constant ℎ Δx × Δp > …..(1) , p = mv …..(2) 2𝜋 ℎ Replace (2) in (1) Δx. Δ(mv), Δx [m Δv + v Δm] , Δm = 0 (no mass exchange, system 2𝜋 ℎ preserved) 2𝜋 ℎ 𝒉 Δx. m.Δv ⩾ 2𝜋 Δx ⩾ 𝟐𝝅𝒎𝚫𝐯 With:  Δv error about speed  Δx: error on the position I.6.3. Wave function and Schrödinger equation: Quantum mechanics no longer takes into account the precise position of the particle but the probability of its presence at a point in space. In 1926 Schrödinger put the fundamental relationship of quantum mechanics in the form of a differential equation: 11  𝟖𝝅²𝒎 𝚫Ѱ + [𝑬 − 𝑽]Ѱ = 𝟎 𝒉² Ѱ : Wave function It is written in reduced form: Δ: Laplacian operator, m the mass of the particle, V (r) the potential energy of the particle at point r. E: Total energy of the particle h: Planck constant The resolution of the Schrödinger equation reveals 4 quantum numbers which are n,l,m,s I.7. Quantum numbers Quantum numbers are : 1. Main quantum number «n» It characterizes the layer (orbit and quantifies the energy of this layer, n= 1, 2, 3, 4, 6, 7…. En= -13.6 Z2/n2 Each level corresponds to a value of n 2. Secondary quantum number «l » It determines the geometric shape of the atomic orbital and it defines an electronic sublayer, for n given, l can take n values so, 0 ≤ l ≤ n-1. l = 0 S orbital 2 electrons l = 1 p orbital 6 electrons l = 2 d orbital 10 electrons l = 3 f orbital 12 3. Quantum magnetic number «m» This number refers to the orientation in space of the atomic orbital in a magnetic field, for the values, m can take 2l+1 value. -l ≤ m ≤ +l 4. Quantum number of spin «s»: It means the direction of rotation of the electron with respect to its axis, by convention an electron is represented by an arrow, an arrow directed upwards, s =+1/2, an arrow directed upwards, s =-1/2. 13  layer n l m Distribution cases spin Nb(é)max K 1 0 0 1S 2 L 2 0 0 2S 8 1 -1, 0,+1 2p M 3 0 0 3S 18 1 -1, 0,+1 3P 2 -2, -1,0,1,2 3d +-1/2 N 4 0 0 4S 32 1 -1, 0,+1 4P 2 -2, -1,0,1,2 4d 3 -3, -2, - 4f 1,0,1,2,3 Note: - For each value of n we have a layer - For each value of n we have a value of n2 boxes. - Each layer contains 2 more cells than the previous one - In the hydrogen atom and hydrogen ions, the orbitals of a given layer have the same energy since the energy depends only on n and not on other quantum numbers. Energy levels are called degenerate. I.8. Orbital filling rules and representation of the electronic structure: The distribution of electrons of the ground state (electronic configuration) in atomic orbitals (OA) is done according to three rules: - Klechkwsky rule - Pauli rule - Hund rule I.8.1. principle of stability: Klechkwsky rule : The electrons of an atom occupy at the ground state the most stable OA, so that of lower energy. Generally, the filling is done in ascending order (n+1) with some exceptions. 14 Klechwsky’s graphic rule allows us to easily remember the order of energy levels. Ascending energy order: 1S